integral is an important topic in the Mathematics section in MHT CET exam. Practising this topic will increase your score overall and make your conceptual grip on MHT CET exam stronger.
This article gives you a full set of MHT CET PYQs for Integral with explanations for effective preparation. Practice of MHT CET Mathematics PYQs including Integral questions regularly will improve accuracy, speed, and confidence in the MHT CET 2026 exam.
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MHT CET PYQs for Integral with Solutions
1.
The solution of the differential equation \( y^2 dx + (x^2 - xy + y^2) dy = 0 \) is- \( \tan^{-1}\left(\frac{x}{y}\right) + \ln y + C = 0 \)
- \( 2 \tan^{-1}\left(\frac{x}{y}\right) + \ln x + C = 0 \)
- \( \ln(v + \sqrt{x^2 + y^2}) + \ln y + C = 0 \)
- \( \ln(x + \sqrt{x^2 + y^2}) + C = 0 \)
2.
$ \int\left[sin \left(log\,x\right)+cos\left(log\,x\right)\right]dx $ is equal to- $ x\, cos (log\,x)+c $
- $ cos (log\,x)+c $
- $ x\, sin (log\,x)+c $
- $ sin (log\,x)+c $
3.
Maximam value of y Subject to : at:- (A) 95
- (B) 90
- (C) 85
- (D) 80
4.
$ \int e^{x} \frac{\left(x-1\right)}{x^{2}} dx $ is equal to- $ \frac{e^{x}}{x^{2}} +c $
- $ \frac{-e^{x}}{x^{2}} +c $
- $ \frac{e^{x}}{x} +c $
- $ \frac{-e^{x}}{x} +c $
5.
\(\int_{-π/2}^{π/2} f(x) \,dx\) =?
Where f(x) = sin |x| + cos |x|, x ∈ \((-\frac {π}{2}, \frac {π}{2})\)- 0
- 2
- 4
- 8
6.
Evaluate the integral: \[ \int \frac{x^2 + 2x}{\sqrt{x^2 + 1}} \, dx \]- \( \frac{1}{3} \left( x^2 + 1 \right)^{3/2} \)
- \( \frac{1}{2} \left( x^2 + 1 \right)^{3/2} \)
- \( \frac{1}{2} \left( x^2 + 1 \right)^{5/2} \)
- \( \frac{1}{3} \left( x^2 + 1 \right)^{5/2} \)
7.
The function f(x) = 2x3 – 9x2 + 12x +29 is monotonically increasing in the interval.- (–∞,∞)
- (–∞,1) U (2, ∞)
- (–∞,1)
- <div>(2, ∞)</div>
8.
The order and degree of the differential equation \( \sqrt{\frac{dy}{dx}} - 4 \frac{dy}{dx} - 7x = 0 \) are respectively- \( 1 \, \text{and} \, \frac{1}{2} \)
- \( 2 \, \text{and} \, 1 \)
- \( -1 \, \text{and} \, 1 \)
- \( 1 \, \text{and} \, 2 \)
9.
If \(\int \frac {2e^x + e^x}{3e^x + 4e^{-x}} \,dx\) = Ax + Blog( 3e2x + 4) + C, then values of A and B are respectively (where C is a constant of integration.)
\(\frac {3}{4}, \frac {1}{24}\)
\(\frac {4}{3}, - 24\)
\(\frac {1}{4}, \frac {1}{24}\)
\(\frac {3}{4}, -\frac {1}{24}\)
10.
∫\(\frac {e^x}{(2+e^x)(e^x +1)}\)dx = (where C is a constant of integration.)
log \((\frac {e^x + 2}{e^x +1})\) + C
log \((\frac {e^x}{e^x +2})\) + C
\((\frac {e^x + 1}{e^x +2})\) + C
log \((\frac {e^x + 1}{e^x +2})\) + C
11.
$ \int\limits_{5}^{10} \frac{1}{\left(x-1\right)\left(x-2\right)}dx $ is equal to- $ log \frac{27}{32} $
- $ log \frac{32}{27} $
- $ log \frac{8}{9} $
- $ log \frac{3}{4} $
12.
The value of the definite integral \( \int_0^{\pi} \sin^2 x \, dx \) is:- \( \frac{\pi}{2} \)
- \( \frac{\pi}{4} \)
- \( \frac{\pi}{3} \)
- \( \frac{\pi}{6} \)
13.
The value of the integral \( \int_0^1 x^2 \, dx \) is:- \( \frac{1}{3} \)
- \( \frac{1}{2} \)
- \( \frac{2}{3} \)
- \( 1 \)
14.
The value of : \( \int \frac{x + 1}{x(1 + xe^x)} dx \).
- \( \log \left| \frac{1 + xe^x} {xe^x} \right| + C \)
- \( \log \left| \frac{xe^x}{1 + xe^x} \right| + C \)
- \( \log \left| xe^x(1 + xe^x) \right| + C \)
- \( \log \left| 1 + xe^x \right| + C \)
15.
∫\(\frac {5(x^6+1)}{X+1}\)dx = (where C is a constant of integration.)
\(\frac {5x^7}{7}\)+ 5x + 5 tan-1 x + c
5 tan–1 x + log (x2 + 1) + C
5(x + 1) + log (x + 1) + C
x5 – \(\frac {5x^3}{3}\) + 5x + C
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